Lesson · Mind, Language and Meaning · Mind

Dualism and the Conceivability Argument

The dualist argues that pain without C-fibre firing is conceivable, so possible, so pain is not the firing of C-fibres. Evaluate the identity claim as a necessity in a small possible-worlds model, with and without the one world the argument needs, and locate the step from conceivable to possible as the decision to include it.

Open the interactive lesson Practice

pain is C-fibres → □(p ↔ c) □(p ↔ c): p ↔ c at every world seen add a world: pain, no C-fibres then □(p ↔ c) is false conceivable → possible admits the world

The argument rests on one world

Core ideas

What this lesson establishes

The conceivability argument is a modal argument, and Identity, Modality and Freedom supplies its instrument. What it adds is a particular world, and a question about the right to put it in.

A true identity holds at every world

If pain is the firing of C-fibres, then wherever there is pain there are firing C-fibres, and the other way round, in every possible case. This is the necessity of identity, and it is what the argument's fourth step asserts. Leibniz's law, met in “Leibniz's Law and the Masked Man”, says that one thing cannot differ from itself in any property; the fourth step adds that it cannot differ from itself from one world to the next. The possible-worlds model of Identity, Modality and Freedom is the instrument that makes that claim checkable, and it is what makes the dualist's argument possible at all.

A zombie world is one more world in the model

A world with pain and no C-fibre firing is not an exotic object. In a model it is a node with p true and c false. Whether such a world exists is the question; what it would do if it did is arithmetic.

Conceivable is not yet possible

That a thinker can imagine a case is a fact about the thinker. That the case is a possible world is a further claim, and the argument needs it as a premise.

The material

From conceivable pain to a false necessity

Four steps, then a model that makes the third one visible.

Definition · Dualism

Dualism about the mind is the claim that mental states are not identical to physical states. The version tested here is about one pair: pain, and the firing of C-fibres in the brain. The claim is not what pain is; it is that pain is not that.

The conceivability argument for it has four steps, and the first three are about what can be imagined.

It is conceivable that there is pain with no C-fibre firing.
Whatever is conceivable in this way is possible.
So it is possible that there is pain with no C-fibre firing.
If pain were identical to C-fibre firing, the two would go together in every possible case. So pain is not identical to C-fibre firing.

Let p say that someone is in pain and c that C-fibres are firing. The identity claim, taken as a necessity, is □(p ↔ c), read “necessarily, p if and only if c”. In a possible-worlds model □A is true at a world when A is true at every world that one can see, so the necessity claim is only as strong as the list of worlds in view.

Here is the model the dualist needs. There are two worlds. The first, w1, is the actual one, and it sees itself and the second.

world sees p c ----------------------- w1 w1, w2 T T w2 none T F

Evaluate at w1. The biconditional p ↔ c is true at w1, where both are true, and false at w2, where p is true and c false. Since w1 sees w2, the claim □(p ↔ c) is false at w1, and the lab prints that value. The lab also lists the worlds where the formula holds: only w2, which sees no world, so nothing there can go wrong. Nothing in the argument turns on that.

Now remove w2. The atoms at w1 are what they were, the formula is what it was, and the verdict reverses: with only w1 in view, □(p ↔ c) is true. No logic changed between the two models. A world was added or taken away. So the work of the argument is done by the second step, which is the licence to add the world.

The dualist can say why the licence is good. We have no access to pain except through how it feels, and how it feels seems to leave open whether anything is going on in the brain. The physicalist answers with a precedent. Before the chemistry, heat without molecular motion was just as easy to imagine, and heat is molecular motion all the same: what was imagined was a situation that felt like heat, not a world without heat. The dualist replies that for pain the way it feels is the thing itself, so no such gap between seeming and being is available. The lab cannot settle that.

The physicalist has a second place to stand, at the fourth step. The first identity theorists held that pain is C-fibre firing as lightning is an electrical discharge, a fact found out and not a necessity, and a contingent identity survives the pain-only world untouched. The argument's answer, which is Kripke's, is that an identity between two things each named for what it is cannot hold here and fail elsewhere, so a physicalist who grants that must fight at the second step instead. The lab writes the identity as a necessity because that is the form the argument gives it, and the model with w1 alone shows what a necessary identity costs the physicalist: nothing, until a world is admitted.

The limit is the usual one. A model has the worlds you gave it. Whether the pain-without-fibres world is a genuine possibility is exactly what the second premise asserts, and the lab computes what follows from the answer, not the answer.

Interactive

Possible worlds

Modal formulas at every world, and the axioms the frame validates

The same claim, with and without one world

The first model has a second world where p is true and c false. Read the value at the first world, then switch to the second model, which keeps only the first world, and read it again. Then try the formula on its own, without the box, in the first model.

Model

Worlds2

Accessibility: 1-2 means w1 sees w2

Valuation: p: 1 2; q: 3

Formula

Evaluate at

Read the box as

Value—

Worlds where it holds—

Frame—

Axioms valid on the frame—

Type [] for the box and <> for the diamond, or use the symbols, with ~ & | -> <-> as usual.

Method

Testing a conceivability argument

Five steps. The fourth is where the premise shows.

Name the two sides

Give the mental state one letter and the physical state another: p for pain, c for C-fibre firing.

State the identity as a necessity

If the two are one thing, they go together everywhere: □(p ↔ c). A mere coincidence of the two here would be p ↔ c and nothing more.

Write down the conceived case

Add a world where p is true and c false, and decide which worlds can see it. That is the dualist's second step, drawn as a node.

Evaluate at the actual world

The necessity claim holds only if the biconditional holds at every world in view. One world where it fails is enough to make it false.

Say which premise admitted the world

If the verdict turns on that world, the argument turns on the claim that it is possible. Name the claim, and say what would count for or against it.

Reading the model

Score 0 / 0

Choose the answer you can justify.

With and without the world

Two models of one formula, □(p ↔ c), read at the actual world w1.

model A: w1 sees w1, w2 p: w1 w2 c: w1 p ↔ c at w1: T at w2: F □(p ↔ c) at w1: False model B: w1 sees w1 p: w1 c: w1 p ↔ c at w1: T □(p ↔ c) at w1: True

The only difference between the models is the second world. The dualist gets a false necessity by admitting it, and the physicalist keeps a true one by declining. What each is entitled to is the question of whether a world that can be pictured is a world that could be.

Common mistakes

Treating what can be conceived as what is possibleThe lab shows what the step costs. With the pain-only world in the model, □(p ↔ c) is false; without it, the same formula over the same letters is true. The argument goes through if the world may be added, and nothing else in it does any work. Whether it may is a claim about possibility, and a claim about what someone can imagine does not decide it: heat was once imagined without molecular motion.

Reading the lab's False as a refutation of physicalismThe lab computed a necessity claim in a model that already includes the world the dualist wants. It reports what follows from that model, and says nothing about whether the world exists.

Reading □A as A at the world you start fromAt w1 the biconditional p ↔ c is true, and □(p ↔ c) is false. A box looks at every world in view, not only at the one you are standing on, and that is why a coincidence here is not a necessity.

Check your understanding

✓

Finish when you can say which world carries the argument.

Given a pair of states and the case a dualist describes, you should be able to build the model with and without the case, evaluate the necessity claim in each, and name the premise that decides between them. An answer that stops at “the argument is bad” has not located anything.

Note: Whether pain is the firing of C-fibres is not what this lesson decides. It teaches where an argument on either side has to commit itself.